HYDRAULIC GRADIENT LINE AND TOTAL ENERGY LINE

We were discussing the concept of laminar and turbulent flow, Reynolds experiment, frictional loss in pipes, derivation of expression for loss of head due to friction in pipes, co-efficient of friction in terms of shear stress, basics of shear stress in turbulent flow and also the minor head losses in pipe flow, in the subject of fluid mechanics, in our recent posts.

Now we will go ahead to see the concept of hydraulic gradient and total energy line, in the subject of fluid mechanics, with the help of this post.

Concepts of hydraulic gradient line and total energy line will be quite useful when we analyze the problems of fluid flow through pipes. Now we will understand here the concept of hydraulic gradient line and total energy line.

Hydraulic gradient line and total energy line are the graphical representation for the longitudinal variation in piezometric head and total head.

Hydraulic gradient line

Hydraulic gradient line is basically defined as the line which will give the sum of pressure head and datum head or potential head of a fluid flowing through a pipe with respect to some reference line.

Hydraulic gradient line = Pressure head + Potential head or datum head

H.G.L = P/ρg + Z

Where,

H.G.L = Hydraulic gradient line

P/ρg = Pressure head

Z = Potential head or datum head

Total Energy Line

Total energy line is basically defined as the line which will give the sum of pressure head, potential head and kinetic head of a fluid flowing through a pipe with respect to some reference line.

Total energy line = Pressure head + Potential head + Kinetic head

H.G.L = P/ρg + Z + V²/2g

Where,

T.E.L = Total energy line

P/ρg = Pressure head

Z = Potential head or datum head

V²/2g = Kinetic head or velocity head

Relation between hydraulic gradient line and total energy line

H.G.L = E.G.L - V²/2g

Let us see the following figure, there is one reservoir filled with water and also connected with one pipe of uniform cross-sectional diameter.

Hydraulic gradient and energy lines are displayed in figure.

At Velocity V = 0, Kinetic head will be zero and therefore hydraulic gradient line and energy gradient line will be same.

At Velocity V = 0, EGL = HGL

Further we will go ahead to find out the basic concept of flow through syphon in the subject of fluid mechanics, with the help of our next post.

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